Coursework solutions for Math 103 Probability: Week 12
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1.
Let denote the event ‘Abel has the live bullet’. Similarly define and , and let denote the event ‘the victim is hit’.
[1 for setting up the events correctly]
Clearly .
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(a)
As partitions the sample space, the law of total probability gives
[0.5 for invoking law of total prob (either writing it in abstract, or stating the name)]
[0.5 for putting correct numbers into the law]
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(b)
By Bayes theorem .
[0.5 for knowing we want , 0.5 for using Bayes’ theorem]
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(a)
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2.
and
The induced sample space for is .
[1 for , 0.5 for correct specification of , 1 for ]
Now
[0.25 for each correct probability]
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3.
The sets , partition .
[1]
Therefore
[2]